Non-dispersive conservative regularisation of nonlinear shallow water (and isothermal Euler) equations

Abstract : A new regularisation of the shallow water (and isentropic Euler) equations is proposed. The regularised equations are non-dissipative, non-dispersive and possess a variational structure. Thus, the mass, the momentum and the energy are conserved. Hence, for instance, regularised hydraulic jumps are smooth and non-oscillatory. Another particularly interesting feature of this regularisation is that smoothed `shocks' propagates at exactly the same speed as the original discontinuous ones. The performance of the new model is illustrated numerically on some dam-break test cases, which are classical in the hyperbolic realm.
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Contributeur : Denys Dutykh <>
Soumis le : vendredi 14 juillet 2017 - 15:37:51
Dernière modification le : lundi 4 décembre 2017 - 15:14:04

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  • HAL Id : hal-01509445, version 3
  • ARXIV : 1704.05290

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Didier Clamond, Denys Dutykh. Non-dispersive conservative regularisation of nonlinear shallow water (and isothermal Euler) equations. 21 pages, 6 figures, 1 table, 35 references. Other author's papers can be downloaded at http://ww.. 2017. 〈hal-01509445v3〉

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